MATH College Algebra Review for Test 1. (d) 3.97 (e) Write each of the following in scientific notation: (a) 0.

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1 MATH 34 - College Algebra Review for Test Section.. Classif each of the following as one or more of the following: natural number, integer, rational number, or irrational number. (a) 5 (b) 7 (c) 2 3 (d) 3.97 (e) Evaluate each of the following: (a) 4 2 2( 3+ 5) (b) Write each of the following in scientific notation: (a) (b) 54, Write each of the following in standard notation: (a) (b) Multipl and give our answer in scientific notation: ( )( 7 ) Rachel s weekl pa increased from $25 to $40. What was the percent change in her weekl pa? Section.2 7. What is the mean of the set of numbers {72, 88, 96, 84}? 8. What is the median of the set of numbers {72, 88, 96, 84}? 9. Find the exact distance between the points (4, 5) and ( 2, ). 0. Find the midpoint of the line segment connecting the points (4, 5) and ( 2, ).. For the relation {( 3,4), (,2), (5, 6)}, (a) what is the domain and (b) what is the range? 2. Give the standard form of the equation of the circle shown at the right. x

2 MATH 34 - College Algebra - Review for Test (Thomason) - p. 2 of 8 3. Give (a) the center and (b) the radius of the circle whose equation is (x 7) 2 + ( + 5) 2 = Give the standard form of the equation of the circle that has its center at (4, 3) with the point (,9) on the circle. 5. Give the standard form of the equation of the circle that has ends of a diameter at ( 3,4) and (7, 6). Section.3 6. (a) Is the set of ordered pairs {(,3),(4,4), (3,)} a function? Explain how ou know. (b) Is the relation whose graph is shown at the right a function? Explain how ou know. x (c) Is the relation given b the following table a function? Explain how ou know. X Y Determine the domain of each of the following functions. 2 (a) f (x) = x 2 (b) g(x) = x (c) h( x) = 3x For f ( x) = x 2 + 5, determine (a) f ( 3), (b) f (4), and (c) f (a + 2). 9. (a) True or False: The graph of 4 +2 = 0 is a vertical line that passes through 3 on the x-axis. (b) True or False: The slope of the line 3x +2 = 0 is undefined. 20. The graph of f is shown at the right. (a) What is the range of f? (b) Determine f ( 2). (c) Determine the value(s) of x for which f (x) = 2 x

3 Section.4 MATH 34 - College Algebra - Review for Test (Thomason) - p. 3 of 8 2. The graph shown at the right shows the price of x ards of carpeting. (a) Find the slope of the graph. (b) Interpret the slope as a rate of change Section x Carpet (square ards) 22. Express the following in interval notation: {x 3 x < 5} 23. Express the following in interval notation: ] ( Use the graph of f at the right to determine the interval(s) in which (a) f is increasing and (b) f is decreasing. Give our answers in interval notation. x 25. For f ( x) = x 2 2x + 3, compute the average rate of change of f from x = 2 to x 2 =. 26. For f (x) = 3x 2 5x + 4, (a) determine f (x + h) and (b) determine the difference quotient f (x + h) f (x) and simplif. h Section (a) Is the data in the table at the right linear? (b) If so, determine the slope-intercept form of the equation of the line passing through the data points? x

4 28. Write a formula for the linear function f show in the graph at the right. MATH 34 - College Algebra - Review for Test (Thomason) - p. 4 of 8 x 29. For f (x) = 3 x + 6, (a) give the slope, (b) give the x-intercept, (c) give the - 2 intercept, and (d) draw the graph. 30. For 4 x + 5 = 20, (a) give the slope, (b) give the x-intercept, (c) give the -intercept, and (d) draw the graph. 3. For 3 = 2, (a) give the slope, (b) give the x-intercept, (c) give the -intercept, and (d) draw the graph. 32. For 2x 0 = 0, (a) give the slope, (b) give the x-intercept, (c) give the -intercept, and (d) draw the graph. 33. For the piecewise function f is defined b f (x) = 4 if x 2, determine x + 3 if x > 2 (a) f ( 3) and (b) f (3). (c) Graph f. Section A person is riding a biccle along a straight highwa. The graph at the right shows the rider s distance in miles from a First Aid Station after x hours. (a) Find the slope-intercept form of the equation of the line. (b) How fast is the bicclist traveling? (c) How far from the First Aid Station was the bicclist initiall? (d) How far from the First Aid Station was the bicclist after 2 hours? (,3) (4,3) x 35. Determine the slope-intercept form of the equation of the line that is perpendicular to = 2 x 2 and that passes through the point (6, ) 3

5 MATH 34 - College Algebra - Review for Test (Thomason) - p. 5 of Determine the slope-intercept form of the equation of the line that is parallel to 3x + 4 =2 and that passes through the point (2, 5). 37. In 2005, the number of homes in the U.S. with flat screen televisions was 7.5 million. Since then, the number of homes in the U.S. with flat screen televisions has been increasing at a constant rate of 8.2 million homes per ear. Let t represent the number of ears since 2005 and write a formula for the linear function N that models this situation. 38. In 2000 there were 7.6 million automobiles produced in the United States and in 2004 there were 6.4 million. The formula V (t) = 0.3t models these data exactl, where t = 0 corresponds to 2000, t = to 200, and so on. Use V (t) to estimate the number of automobiles manufactured in the U. S. in In 998 the value of a house was $50,000 and in 2006 the value of the house was $82,000. Find a linear function V that approximates the value of the house in ear x. 40. Suppose is direction proportional to x and that =2 when x = 7. Find if x =0. 4. The cost of tuition is directl proportional to the number of credit hours taken. If 2 credit hours cost $528, what would be the cost of 5 credit hours. Section Solve the equation: 2(3x 4) 5 = 6 (x ) 43. Solve the equation: 2 3 x 3 4 = 5 6 x Solve for b: 3a 5b = Jell Beans sell for $2 a pound and Gumm Bears sell for $3 a pound. How man pounds of each kind of cand must be used to produce a 0 pound mixture worth a total of $27.50? 46. Suppose Joe, working alone, can rake a certain lawn in 4 hours and that John, working alone, can rake the same lawn in 8 hours. How long would it take Joe and John working together to rake the same lawn? 47. A rectangular window has a length that is 8 inches more than its width. The perimeter of the window is 00 inches. Find the length and width of the window. 48. A car went 30 miles in 5 hours, traveling part of the time at 55 miles per hour and part of the time at 65 miles per hour. For what length of time did the car travel at each speed? Section Solve for x and give the solution in interval notation: 2(3x 5) + 4 > 2x Solve for x and give the solution in interval notation: 7 < 2x + 5

6 5. Solve and give our solution in interval notation: 3x 5 4 MATH 34 - College Algebra - Review for Test (Thomason) - p. 6 of The total cost of producing x copies of a CD is given b = x. For what number of CDs will the total cost be between $3,75 and $3,900? Section Graph = 3x Solve: 4 x 5 = Solve: 2x 3 = Solve: 3x 4 = 5x Solve and give the solution in interval notation: 5x 8 < Solve and give the solution in interval notation: 2x 5 Answers. (a) integer, rational number (b) irrational number (c) rational number (d) rational number < 7 2. (a) 44 (b) 8 3. (a) (b) (a) (b) 92, % (, 3). (a) { 3,,5} (b) { 4,2, 6} 2. (x +) 2 + ( +) 2 = 9 3. (a) ( 7, 5) (b) 2 4. ( x 4) 2 + ( + 3) 2 =69 5. ( x 2) 2 + ( +) 2 = (a) Yes, because no first number in the ordered pairs is repeated as a first number. (b) No, because the graph fails the Vertical Line Test. (c) No, because 3 is repeated as a first number in the ordered pairs. 7. (a) { x x 5,5} (b) { x x is a real number} (c) x x (a) 4 (b) (c) a 2 4a + 9. (a) F (b) T 20. (a) { x 0 x 3} (b) 3 (c) 3,, 3 2. (a) 7 (b) Carpet cost $7 per sq d.

7 MATH 34 - College Algebra - Review for Test (Thomason) - p. 7 of [ 3,5) 23. (, ] (2, ) 24. (a) (, ] [3,4] (b) [,3] [4, ) (a) 3x 2 + 6hx + 3h 2 5x 5h + 4 (b) 6x + 3h (a) Yes (b) = 4 3 x (a) 3 2 (b) (4,0) (c) (0,6) 30. (a) 4 5 (b) ( 5,0) (c) (0,4) 28. = 2 3 x (a) 0 (b) none (c) (0, 4) 32. (a) undefined (b) (5,0) (c) none 33. (a) 4 (b) (a) = 6x + 7 (b) 6 mph (c) 7 mi (d) 9 mi 35. = 3 2 x = 3 4 x N (t ) = 8.2t million (c) 39. V (t ) = 4000x 7,842, $ a 8 5

8 lb of Jell Beans, 7.5 lb of Gumm Bears MATH 34 - College Algebra - Review for Test (Thomason) - p. 8 of hr 47. Length: 29 in., Width: 2 in hr at 55 mph, 2.6 hr at 65 mph 49., [ 3,6) 5. 3, 52. Between 35 and 280 CDs. 54.,3 55. No solution , (,2] [ 3, ) ,2